# Page:Carroll - Game of Logic.djvu/42

26
[Ch. I.
NEW LAMPS FOR OLD.

tribute belonging to the 'Middle Terms', we will let ${\displaystyle m}$ stand for "canny",${\displaystyle x}$ for "Dragons", and ${\displaystyle y}$ for "Scotchmen". So that our two Premisses are, in full,

 "All Dragon-Animals are uncanny (Animals); ${\displaystyle \scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}}$ All Scotchman-Animals are canny (Animals)."

And these may be expressed, using letters for words, thus:

 "All ${\displaystyle x}$ are ${\displaystyle m^{\prime }}$; ${\displaystyle \scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}}$ All ${\displaystyle y}$ are ${\displaystyle m}$."

The first Premiss consists, as you already know, of two parts:

"Some ${\displaystyle x}$ are ${\displaystyle m^{\prime }}$,"

and "No ${\displaystyle x}$ are ${\displaystyle m}$."

And the second also consists of two parts:

Some ${\displaystyle y}$ are ${\displaystyle m}$,"

and "No ${\displaystyle y}$ are ${\displaystyle m^{\prime }}$."

Let us take the negative portions first.

We have, then, to mark, on the larger Diagram, first, "no ${\displaystyle x}$ are ${\displaystyle m}$", and secondly, "no ${\displaystyle y}$ are ${\displaystyle m^{\prime }}$". I think you will see, without further explanation, that the two results, separately, are

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